Analysis of an iterative scheme of fractional steps type associated to the reaction–diffusion equation endowed with a general nonlinearity and Cauchy–Neumann boundary conditions

The paper studies the existence, uniqueness, regularity and the approximation of solutions to the reaction–diffusion equation endowed with a general nonlinear regular potential and Cauchy–Neumann boundary conditions. The convergence and error estimate results for an iterative scheme of fractional steps type, associated to the nonlinear parabolic equation, are also established. The advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation.